C₂₃×#2123 #15669742

order	2944
nilpotency class	4
isoclinism	isoclinic class of #2121
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₂₃ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₂₃×#2123

Subgroups

	subgroup	G/H
center, socle	C₂×C₂₃	C₂×#99
commutator	C₂³	C₂²×C₄×C₂₃
Frattini, cosocle	C₂×D₄	C₂³×C₂₃
prime radical	C₂×#41×C₂₃	C₂²
LCS	G ▷ C₂³ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₂₃ ◁ C₂×C₄×C₂₃ ◁ C₂×#41×C₂₃ ◁ G

234 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 84 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

minimal degree	μ(G) = 55
transitive degree	μ_t(G) = 736

A minimal faithful permutation representation — 3 generators on 55 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23)(24,25)(26,34)(27,31)(28,41,42,32)(29,33)(30,36,44,51)(35,48)(37,49)(38,52)(39,54,55,46)(40,47)(43,50,45,53);(24,26,29,37)(25,30,33,44)(27,38,40,35)(28,36,42,51)(31,45,47,43)(32,34,41,49)(39,53,55,50)(46,52,54,48);(24,27,29,40)(25,31,33,47)(26,35,37,38)(28,39,42,55)(30,43,44,45)(32,46,41,54)(34,48,49,52)(36,50,51,53)

Conjugacy classes & character table

529 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₃×#12716, C₂₃×#12717, C₂₃×#12723, …
maximal normal subgroup of	C₂₃×#12716, C₂₃×#12717, C₂₃×#12723, …
maximal quotient of	C₂₃×#11428, C₂₃×#11454, C₂₃×#11474, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 855);